I think that it very much depends on what you want to store in the database. I don't have experience with CouchDB or Cassandra so I will let someone else speak for them but I frequently use MongoDB and MySQL.
If you were developing application that required transactions e.g. a billing application you would definitely want to use MySQL because of its support for transactions. MySQL is ACIDic that is it is Atomic, Consistent, Isolated and Durable. What that essentially means is that when you update a row in MySQL - it is GUARANTEED to have happened. However the issue with MySQL is that it does not scale horizontally (by adding more and more servers) very easily. MySQL servers tend to be scaled vertically by adding more memory, HDD space etc but they eventually hit a ceiling and it can reach an enormous cost.
MongoDB is a document database. It stores JSON-like documents inside collections and is schema-less - so each document can be different. This is great for flexibility in your application. A lot of developers say that noSql solutions are developed more for programmers and they tend to be much easier to build with (in my experience). In addition MongoDB scales horizontally by sharding the database into chunks. In fact this can even be automated now.
But there are drawbacks to using MongoDB. If you are using it in production you really MUST put in a replication slave with it. This is because MongoDB does not have full single server durability. So if you suffer a power failure you will probably have to repair the entire MongoDB database which can take hours. This is probably not a big deal cost-wise if you are well-funded but if you are a new organisation with little money it can be difficult (use cloud computing? ). In addition MongoDB does not support transactions which is necessary to guarantee Atomicity and Isolation. Finally MongoDB is only eventually consistent (though I have seen a few sides to this argument) - which means that when a write happens all other processes are not GUARANTEED to see the information straight away - only eventually.
In my opinion if you are storing artist information and meta-data about tracks then MongoDB would be a good solution. If you were storing user data, billing data etc then store it in MySQL.
